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Block #3,227,456

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/16/2019, 6:57:40 AM Β· Difficulty 11.0071 Β· 3,606,228 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
11dff5b2d061852c51ad32b540a3ce5d3a445c6ad154cecd2a16a21df1426b3a
View on Chainz β†—

Height

#3,227,456

Difficulty

11.007119

Transactions

2

Size

572 B

Version

2

Bits

0b01d291

Nonce

2,143,379,473

Timestamp

6/16/2019, 6:57:40 AM

Confirmations

3,606,228

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

fcabcf48bb5c7997d2fa37e9a66931ffd7c146b86eacc2b62da20235ec15c393
Transactions (2)
Coinbase37515485583369…72df927fc878db
1 in β†’ 1 out8.2500 XPM110 B
ARbm48qR…9xQc8DBX
0db62e8e6f9351…feb1113b399d24
2 in β†’ 2 out963.3089 XPM372 B
AeTHTL7A…vT1872bkARwgrpDB…Qn8oiHVW
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.164 Γ— 10⁹⁡(96-digit number)
21644350891683807488…30826067103901274241
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
2.164 Γ— 10⁹⁡(96-digit number)
21644350891683807488…30826067103901274241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.328 Γ— 10⁹⁡(96-digit number)
43288701783367614977…61652134207802548481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.657 Γ— 10⁹⁡(96-digit number)
86577403566735229955…23304268415605096961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.731 Γ— 10⁹⁢(97-digit number)
17315480713347045991…46608536831210193921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.463 Γ— 10⁹⁢(97-digit number)
34630961426694091982…93217073662420387841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.926 Γ— 10⁹⁢(97-digit number)
69261922853388183964…86434147324840775681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.385 Γ— 10⁹⁷(98-digit number)
13852384570677636792…72868294649681551361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.770 Γ— 10⁹⁷(98-digit number)
27704769141355273585…45736589299363102721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.540 Γ— 10⁹⁷(98-digit number)
55409538282710547171…91473178598726205441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.108 Γ— 10⁹⁸(99-digit number)
11081907656542109434…82946357197452410881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.216 Γ— 10⁹⁸(99-digit number)
22163815313084218868…65892714394904821761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
4.432 Γ— 10⁹⁸(99-digit number)
44327630626168437737…31785428789809643521
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,913,692 XPMΒ·at block #6,833,683 Β· updates every 60s
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